How can I check for homogeneity of variance in a factorial anova design? | Stata FAQ

To analyze a factorial anova you would use the anova command. The anova command does not have a check for homogeneity of variance. However, the oneway command automatically performs a Bartlett’s test for homogeneity of variance along with a one-way anova. The trick is to convert your factorial design into a one-way design.

Let’s say that you want to run a 2×4 factorial using the file crf24.dta. The following commands will illustrate the process:

use https://stats.idre.ucla.edu/stat/stata/faq/crf24
anova y a b a#b

   Number of obs =      32     R-squared     =  0.9214
   Root MSE      = .877971     Adj R-squared =  0.8985

  Source |  Partial SS    df       MS           F     Prob > F
---------+----------------------------------------------------
   Model |      217.00     7       31.00      40.22     0.0000
         |
       a |       3.125     1       3.125       4.05     0.0554
       b |      194.50     3  64.8333333      84.11     0.0000
     a*b |      19.375     3  6.45833333       8.38     0.0006
         |
Residual |       18.50    24  .770833333   
---------+----------------------------------------------------
   Total |      235.50    31  7.59677419  

Now enter these commands:

egen cell = group(a b)
robvar y, by(cell)

            |            Summary of y
 group(a b) |        Mean   Std. Dev.       Freq.
------------+------------------------------------
          1 |        3.75         1.5           4
          2 |           4   .81649658           4
          3 |           7   .81649658           4
          4 |           8   .81649658           4
          5 |        1.75          .5           4
          6 |           3   .81649658           4
          7 |         5.5   .57735027           4
          8 |          10   .81649658           4
------------+------------------------------------
      Total |       5.375   2.7562246          32

W0  = .74805195   df(7, 24)     Pr > F = .63460714

W50 = .13714286   df(7, 24)     Pr > F = .99422247

W10 = .74805195   df(7, 24)     Pr > F = .63460714

The variable cell created using the egen command takes on the values 1 through 8.  The robvar command gives you Levene’s test of homogeneity (labeled W0).

Note:  Levene’s test is relatively more robust to nonnormality than other tests of homogeneity but can still be influenced by nonnormality and should be used with caution.